Factoring Polynomials

Front

What is factoring in mathematics?

Back

Factoring is the process of breaking down an expression into a product of simpler factors that, when multiplied together, give the original expression.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

Front

What is the greatest common factor (GCF)?

Back

The greatest common factor (GCF) is the largest factor that divides two or more numbers or expressions without leaving a remainder.

Front

How do you factor a polynomial expression?

Back

To factor a polynomial expression, identify common factors, use special factoring formulas (like difference of squares), or apply methods such as grouping or synthetic division.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a² - b² = (a - b)(a + b).

Front

What is the process to factor a trinomial of the form ax² + bx + c?

Back

To factor a trinomial of the form ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the middle term and factor by grouping.

Front

What is the significance of the leading coefficient in polynomial factoring?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It affects the shape and direction of the graph of the polynomial.

Front

What is synthetic division and when is it used?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c).

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms, such as a + b or x² - 4.

Front

What is the factor theorem?

Back

The factor theorem states that if a polynomial f(x) has a factor (x - c), then f(c) = 0.